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Marginal underdominance at a stable equilibrium.

A Hastings1

  • 1Department of Mathematics, University of California, Davis, California 95615.

Proceedings of the National Academy of Sciences of the United States of America
|October 1, 1981
PubMed
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A stable equilibrium in a two-locus genetic model was identified where marginal underdominance occurs. This finding was achieved through a numerical search for specific fitness values leading to this equilibrium.

Area of Science:

  • Population genetics
  • Mathematical biology
  • Evolutionary genetics

Background:

  • Population genetics models explore how allele and genotype frequencies change over time.
  • Stable equilibria are crucial for understanding the long-term genetic makeup of populations.
  • Underdominance, where heterozygotes have lower fitness, can complicate evolutionary trajectories.

Purpose of the Study:

  • To demonstrate a stable equilibrium in a two-locus, two-allele genetic model.
  • To investigate conditions under which marginal underdominance can be maintained.
  • To provide a concrete example of a specific genetic equilibrium.

Main Methods:

  • Development of a deterministic, discrete-generation model with two loci and two alleles.
  • Utilizing a numerical search procedure to identify equilibria.

Related Experiment Videos

  • Testing various fitness assignments to locate equilibria exhibiting marginal underdominance.

    • Main Results:

    • An example of a stable equilibrium was successfully identified within the specified model.
    • This equilibrium is characterized by the presence of marginal (or induced) underdominance.
    • The numerical search effectively located fitness configurations supporting this specific equilibrium.

    Conclusions:

    • It is possible to establish stable equilibria in two-locus genetic models even with marginal underdominance.
    • Numerical search methods are effective tools for discovering specific genetic equilibrium configurations.
    • The findings contribute to a deeper understanding of complex genetic dynamics and stability in populations.